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Maximizing expected value with two stage stopping rules

Author

Listed:
  • David Assaf
  • Larry Goldstein
  • Ester Samuel-Cahn

Abstract

Let X n ,…,X 1 be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let V n 2 equal the expectation of the larger of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence V n 2 for a large class of F's belonging to the domain of attraction (for the maximum) D(G II ? ), where G II ? (x) = exp(-x -? )I(x > 0) with ? > 1. The results are compared with those for the asymptotic behavior of the classical one choice value sequence V n 1 , as well as with the "prophet value" sequence E(max{X n ,…,X 1 }), and indicate that substantial improvement is obtained when given two chances to stop, rather than one.

Suggested Citation

  • David Assaf & Larry Goldstein & Ester Samuel-Cahn, 2004. "Maximizing expected value with two stage stopping rules," Discussion Paper Series dp351, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp351
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    Cited by:

    1. Larry Goldstein & Ester Samuel-Cahn, 2004. "Optimal Two Choice Stopping on an Exponential Sequence," Discussion Paper Series dp375, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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